Remove the trap and rod straight into the wall with a 1/4" snake. Inspcet the trap too.

Disassemble the trap under the sink and see where the blockage is. You might be able to snake through the wall fitting.

Have you tried, bleach, it eats away at nearly everything

The problem with pouring chemicals down the drain is that they are trapped in a blockage and then a plumber or someone else has to deal with lye, drano, bleach etc.

Ohh sorry! (: